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NastyaMoore
@NastyaMoore
July 2022
1
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опрелелите первый член и знаменатель геометрической прогрессии если изанстно что разность между третьим и вторым членом равна 12 а сумма удвоенного третьего члена и четвертого члена равна 96
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Dимасuk
Verified answer
B3 - b2 = 12
2b3 + b4 = 96
b1q² - b1q = 12
2b1q² + b1q³ = 96
b1q(q - 1) = 12
b1q(2q + q²)= 96
b1q = 12/(q - 1)
b1q = 96/(2q + q²)
12/(q - 1) = 96/(2q + q²)
24q + 12q² = 96q - 96
2q + q² = 8q - 8
q² - 6q + 8 = 0
q1 + q2 = 6
q1•q2 = 8
q1 = 2 и q2 = 4
b1q(q - 1) = 12
b1•2(2 - 1) = 12
b1 = 6
и
b1•4(4 - 1) = 12
b1 = 1
Ответ: b1 = 1, q = 4 иди b1 = 6, q = 2.
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Answers & Comments
Verified answer
B3 - b2 = 122b3 + b4 = 96
b1q² - b1q = 12
2b1q² + b1q³ = 96
b1q(q - 1) = 12
b1q(2q + q²)= 96
b1q = 12/(q - 1)
b1q = 96/(2q + q²)
12/(q - 1) = 96/(2q + q²)
24q + 12q² = 96q - 96
2q + q² = 8q - 8
q² - 6q + 8 = 0
q1 + q2 = 6
q1•q2 = 8
q1 = 2 и q2 = 4
b1q(q - 1) = 12
b1•2(2 - 1) = 12
b1 = 6
и
b1•4(4 - 1) = 12
b1 = 1
Ответ: b1 = 1, q = 4 иди b1 = 6, q = 2.